Question

Tính:

S = 1+4+4²+4³+...+4¹⁰⁰

Answer 1

S=1+4+4²+4³+…+4¹⁰⁰

=>S.4=4+4²+4³+4⁴+…+4¹⁰¹

=>S.4-S=4+4²+4³+4⁴+…+4¹⁰¹-1-4-4²-4³-…-4¹⁰⁰

=>S.3=4¹⁰¹-1

=>\(S=\frac{4^{101}-1}{3}\)

Answer 2

S=1+4+4²+4³+...+4¹⁰⁰

=>4S=4+4²+4³+4⁴+...+4¹⁰¹

=>4S-S=(4+4²+4³+...+4¹⁰¹)-(1+4+...+4¹⁰⁰)

=>3S=4¹⁰¹-1

=>\(S=\frac{4^{101}-1}{3}\)

vậy \(S=\frac{4^{101}-1}{3}\)